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2. (10 points) We flip a fair coin. If the outcome is heads we roll 3 fair dice. If it the outcome is tails we

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2. (10 points) We flip a fair coin. If the outcome is heads we roll 3 fair dice. If it the outcome is tails we roll 5 fair dice. Let X denote the number of sixes among all rolled dice. (a) Find the probability mass function of X. (b) Find the expected value of X

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